What part of his life does our narrator believe his “stern and black-browed Puritan” ancestors would never have understood / completely disapproved of? Why?

I think this is referring to the character of Pearl who represents a dimension of Hawthorne's own "creative force" which allows him to rebel against his "stern and black-browed" puritan fathers who, in his own mind, rebuke him as a "writer of story-books." Pearl is the embodiment of innocence and imagination which the Puritans of Hawthorne's past could not comprehend. She is Hawthorne's sort of revenge against his ancestors who would have not considered him a writer.